COMPARISON OF ATTENUATION AND PHASE VELOCITY MEASUREMENTS IN

Transcription

1 COMPARISON OF ATTENUATION AND PHASE VELOCITY MEASUREMENTS IN COMPOSITES MADE USING UNIPOLAR AND BIPOLAR PULSES INTRODUCTION M. S. Hughes 1, D. K. Hsu 1, S.J. Wormleyl, J. M. Mann 1, C. M. Fortunk 2, and D. O. Thompson 1 1Center for NDE Iowa State University Ames, IA 511 2Air Scan Corp. 919 Sunset Drive Costa Mesa, CA We have made a comparison of the ultrasonic attenuation coefficient and phase velocity obtained from two different experimental systems. The first set-up employed unipolar (either one relative maximum or minimum) ultrasonic pulses to interogate a speeimen of porous woven graphite/epoxy composite. In the second, bipolar (one relative maximum and one relative minimum) ultrasonic pulses were used to interogate the same speeimen. The replacement of bipolar pulses by unipolar pulses lead to an increase in fractional bandwidth of at least 2% for measurements of both phase veloeity and attenuation coeffieient. Most of this inerease arose from improvements in sensitivity at lower frequencies. Gains of this nature will signifieantly improve the stability of flaw inversion algorithms in either thick composites or porous eomposites where attenuation los ses prevent the acquisition of data at high frequeneies. Use of unipolar pulses also doubles the temporal (spatial) resolution that may be obtained using ultra sound generated by any partieular transducer; this is a eonsequenee of the fact that the unipolar pulse will be one half as long as the bipolar pulse produeed by the same transdueer. Inereased resolution will permit eharaeterization of thinner eomposites than may be analyzed with presently available bipolar inspection equipment. In addition, unipolar pulses may offer improved ability to deteet aeoustie impedanee gradients[l] and may thus find applieations in the analysis of two phase systems. BACKGROUND Conventional broadband ultrasonic inspection techniques are based on the use of bipolar pulses. However, pulses with an even greater number of relative maxima and minima are frequently employed. The greater the number of relative extrema the smaller the bandwidth. This can be seen by noting that a tripolar pulse may be obtained from a bipolar pulse by differentiation, that a quadrupolar pulse may be obtained by differentiating a tripolar pulse and so on. Operationally, this differentiation is equivalent to highpass filtering the reeeived ultrasonic signal and thus has the effeet of redueing signal sensitivity at the lower end of the bandwidth of the inspeetion system. 1111

2 Maximum bandwidth may be obtained if this transmitted waveform is composed of just one relative maximum (minimum). In this case the spectral energy distribution of the wave pulse will extend down to D.C. This idealization can only be approximated for immersion bath measurments since the presence of a true D.C. component would imply mass transport in the system. In addition, any ultrasonic system employing piston source transducers will have a radiation pattern in which low frequencies suffer greater diffraction los ses than do the high frequency components of the emitted waveform. Consequently, even if a perfectly unipolar waveform is generated it will evolve into abipolar waveform due to the high-pass filtering effects it experiences as it propagates. Such effects can be minimized to some extent by placing the transmitting and receiving transducers in close proximity to each other. This is the approach adopted for the purposes of our study. APPROACH For our study a.31 cm thick specimen of woven graphite/epoxy composite (density = 1.59 gm/cm, with 3.41% volume fraction of porosity) was insonified at perpendicular incidence. The frequency dependent attenuation coefficient was measured in transmission-mode using the technique of log-spectral-subtraction[2]. The phase velocity was measured, also in transmission-mode, using the technique of ultrasonic phase spectrscopy[3]. UNIPOLAR VS. BIPOLAR PULSE GENERATION Both a Ritec BP94 pulser with a square wave output (Amplitude = 4 V, pulse duration = 7 ms, 2 ns transition from 4 V to ground) and a QMI Square wave pulser (Amplitude = -4 V, pulse duration = 7 ms, 15 ns transition from ground to -4 V) were used to exeit unipolar pulses in a piezoelectric transducer (Panametrics V11,.25" dia., 5. MHz center frequency). The pulses generated by the falling (Ritec BP94) or rising edge (QMI Pulser) of this excitation were used for this study. The duration of the Squarc Wave Pulser Conventional Pulser Transmitter W a ter Tank Receiver Sampli ng Digital O scilliscope CHI Trig Controller/Computer Fig. 1 Diagram of the apparatus used to carry out a eomparison of phase velocity and attenuation for both unipolar and bipolar pulses.,,, 2

3 / Transmitter ::;~: ~!~!~~ili \ Receiver Reference Trace 2mm --l I-- / SampIe SampIe Trace Fig. 2 A diagram showing the two types of time domain traces required for the measurement of frequency dependent attenuation and phase velocity. The top portion of Fig. 2 shows the acquisition of a reference tr'ace used to calibrate out instrumental effects. The bottom portion of the figure shows the acquisition of a sample trace. square wave excitation was made long enough to avoid interference from the ultrasonic pulses generated by the rising edge (Ritec BP94), or falling edge (QMI Pulser), of the applied excitation. In this way a good approximation to the perfect step function excitat ion, required for the generation of a unipolar pulse, was obtained. The transmitted ultrasound was received by a.75" 5. MHz Center Frequency PZT transducer (Panametrics Vl15) placed 7 cm from the transmitting transducer. A panameterics 552/PR pulser was used to generate bipolar pulses in the same transmitting transducer as was used for the unipolar pulse measurements. In this case, the pulse is generated by a negative going spike (Amplitude = -175 V, duration < l~s) which is considered to be a good approximation to a delta function. The apparatus used for the diagram is indicated in Fig. 1. As the figure indicates the only difference between the unipolar and bipolar systems is the type of pulser used to drive the transducer, all other aspects of the two systems are identical. METHODS Both attenuation coefficient and phase velocity measurements require the acquisition of two types of time domain traces. The first is a reference trace which contains the system response of the experimental apparatus. The second is a sampie trace which 1113

4 contains the system response of the experimental specimen. Both types of traces were acquired using a water bath as shown in Fig. 2. These traces were then transformed to the frequency domain and the magnitudes and unwrapped phases, phase ref (CO) and phase ample (CO)'. computed. From these data the phase veloclty was computed accordlng to. where CO = 21tf, v is the velocity of sound in water, and d is the sampie thickness. Using these phase velocity data the acoustic impedance of the sampie, Z = PC(CO), was computed and used to correct the magnitude of the sampie trace for insertion los ses using the formula [ (1) 4Z wzs ]2 (2) Magsarrp1e,aorrected(c.o) = 1-2 Magsarrple,uncorrected(c.o) (Zw+ Zs). '"' ' 1.2.~ ca.8 r:: '-".4 ca. r:: bo CI) ' ;> 'ö C,,) CI:: Water Only Path Data Point Number Fig. 3 '"' ' 1.2 N ~.8.4 r:: '-" «l c. bo CI) -.4 ' ;> 'ö -.8 C,,) CI:: "1.2 Water Only Path lfvvr Data Point Number A comparison of pulses obtained from a conventional pulser and a step function pulser. The top portion of the figure shows a bipolar pulse obtained using a Panametrics 552 pulser receiver. The bottom half of the figure shows a quasi-unipolar pulse obtained using a Ritec BP94 step function pulser. The imperfections in the pulse are due to diffraction los ses in the low frequency portion of transmitted wave. 1114

5 where Z is the acoustic impedance of water (we note that Eq.2 gives the compensated magnitude in terms of the uncompensated magnitude for either particle velocity or pressure). The attenuation coefficient was then computed from the magnitude of the reference trace, Mag f(ffi), and the corrected sampie magnitude, Mag ::rnple,corrected (ffi), according to DISCUSSION attenuation «) log [magref (ffi) - Magsarnple, corrected (ffi) lid, (3) The reference data acquired for the comparison of unipolar and bipolar systems are shown in Fig. 3. The trace in the top panel of Fig. 3 was obtained using the conventional pulser and is clearly bipolar. The positive peak of the received signal is nearly equal in magnitude to that of the negative portion of the pulse. However, the reference trace obtained using the square wave pulser, shown in the bottom panel of Fig. 2, exhibits a positive peak which is 2.5 times greater than the negative portion of the peak. This negative portion of the received signal arises from several causes. Perhaps the most important are diffraction losses which high-pass-filter the transmitted pulse. The time domain data shown in Fig. 2 were Fourier transformed and the magnitudes and unwrapped phases were computed. The sampie magnitude data for both systems are compared in Fig. 4 which shows the uncorrected sampie magnitude data sets plot ted against a logarithimic frequency scale. Both the unipolar and the bipolar magnitude traces have been normalized to their respective peak amplitudes; thus, differences in pulser output voltage have been removed to allow a fair comparison of the outputs of both systems. The upper limit of the useful bandwidth, about 1 MHz, is the same for both data sets. However, the unipolar data set extends to a lower frequency of 2 khz versus 5 khz for the bipolar system. The unipolar system thus exhibits a 5% increase in fractional bandwidth (upper bound of bandwidth/lower bound of bandwidth) over that obtained using the bipolar pulses. The same conclusion may be drawn from a comparison of the reference magnitudes obtained from both systems. Figure 4 shows that the frequency domain data obtained using the unipolar pulses have relatively more energy at low frequencies than the data obtained from the bipolar pulses. In addition, the unipola~ pulser system has greater energy output at higher frequencies. This is due to the larger excitation voltage used in the unipolar system. This point is illustrated in Figure 5 which shows a comparison of the sampie magnitude data obtained from both systems. Both curves have been normalized to the output voltage of the step function pulser used in the unipolar system. This normalization was accomplished by first normalizing each curve to its respective peak and then by rescaling the bipolar system magnitude curve by the ratio of the output voltages of the two systems; ratio = 175/4. As Fig. 5 shows, the energy output by the unipolar system is greater than that output by the bipolar system in absolute, as weil as relative, terms. Furthermore, the energy output of the unipolar system remains greater than the output by the bipolar system at high frequencies as weil. Thus, the unipolar system offers two improvements over the bipolar system; fractional bandwidth is increased by 5% and system sensitivity is increased over the entire usable bandwidth of the system. Fractional bandwidth was chosen as the relevant parameter for characterizing system performance, based on the requirements for stable flaw inversion algorithms. The range of frequencies required for stable inversion must span ka =.5 to 2.5 where ka = 2 nfa/v, a = flaw diameter, and v = velocity of sound in the host medium. Thus, to accurately size a flaw with a diameter of a = 1!!I1l requires a bandwidth extending from 1 to 5 MHz; to size a flaw of a = 5 ~m requires a bandwidth extending from 2 to 1 MHz. The upper 111 5

6 bound of the bandwidth is fixed by the center frequency of the transmitting transducer and is the same for both bipolar and unipolar systems (see fig. 5). Only the lower bound of the bandwidth changes, depending on which pulser is used. Thus the ratio, f If i = fractional bandwidth, is sufficient to determine whether tne requirement for stable flaw inversion is satisfied. : cl) N oa E S cl) " a., 2: '2 r>i) Unipolar Frequency (MHz) Unipolar Frequency (MHz) Fig. 4a Top panel. A comparison of the energy content of the received ultrasound obtained from the conventional pulser and the step function pulser. Both magnitude curves have been normalized to their peak amplitudes to permit fair comparison of the curves in spite of the different pulser voltages used in both systems. Fig. 4b Bottom panel. A comparison of the energy content of the received ultrasound obtained from the conventional pulser and the step function pulser. Both magnitude curves have been normalized to the peak amplitude of the step function pulser (4 v) to permit an absolute comparison of the energy output by both systems at each frequency. 1116

7 15 - Unipolar Data Bipolar Data E "-' c::.9 C;; ::l c:: ~.;;: 1 5 Freq min=.292 MHz OL...-_-~... _~-~~~ Freq/Freqmin Fig. 6 A comparison of the attenuation curves obtained using unipolar pulses with those obtained using bipolar pulses. The unipolar based data has a fractional bandwidth which is approximately 3 times that of the bipolar based data. The magnitude data are used to compute the attenuation coefficient according to Eq. 3. The resulting curves for both the unipolar and bipolar data are plotted in Figure 6 against a logarithmic frequency axis which has been normalized to a reference frequency Freq min. The reference frequency of Freqmin =.292 MHz has been chosen as a cut toff for the range over which the attenuation coefficient has been reliably determined; below this frequency the standard errors associated with each data point are greater than 5% of the measured value, above this point the associated standard errors are all less than 5% (in fact they are all less than 3 %). As we would expect from the plots in Figures 4 and 5 this cutoff is determined by the unipolar data set which extends to lower frequencies than do the data sets obtained using bipolar pulses. Only data points for which the associated standard error is less than 1% are plotted. As the plot shows the curve obtained using the unipolar system extends to lower frequencies. Figure 7 shows a similar comparison of the phase velocity data sets obtained from the bipolar and unipolar systems. Even using conservative criterion for acceptance of valid data that has been adopted in Figures 6 and 7 we see that the unipolar system has twice the bandwidth of the bipolar system. 1117

8 Unipolar Data 3 Bipolar Dala / ~ 28 :g '".' ~ 'ü 26,. -f :; > 24..,.c '" "" Frcqmin=O.292 MHz 18 I 1 1 Freq/Freq "';. Fig. 7 A comparison of the phase velocity curves obtained using unipolar pulses with those obtained using bipolar pulses. The the unipolar based data has a fractional bandwidth which is approximately 3 times that of the bipolar based data. CONCLUSIONS The use of unipolar pulses allows significant improvements in the bandwidth, with the greatest improvement occuring at lower frequencies. This improvement can be used to increase the reliability of flaw characterization, e.g. determination of porosity, in composite materials. The significant improvements in sensitivity observed at lower frequencies suggests that this approach will be particularly useful in thick composites where the ability to make reliable measurements is limited by attenuation losses. ACKNOWLEDGEMENTS This work was supported under Department of Commerce Grant No. ITA and was carried out under the auspices of the Center for New Industrial Materials at Iowa State University. REFERENCES 1. D. O. Thompson and D. K. Hsu, "Technique for Generation of Unipolar Ultrasonic Pulses," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 35, No.4, pp J. Ophir, T.H. Shawker. N.F. Maklad, J.G. Miller, S.W. Flax, P.A. Narayana, and J.P. Jones, "Attenuation Estimation in Reflection: Progress and Prospects,"Ultrasonic Imaging, vol. 6, pp , W. Sachse and Y.H. Pao, "On the Determination of Phase and Group Velocities of Dispersive Waves in Solids," Journal of Applied Physics, vol. 49, pp ,